Universal distribution of threshold forces at the depinning transition

Fedorenko, Andrei A.; Doussal, Pierre Le; Wiese, Kay Joerg

doi:10.1103/physreve.74.041110

Cited by 34 publications

(68 citation statements)

References 45 publications

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“…Since ζ F SR < ζ SR , a finite g guarantees that at high T the system is described by the SR fixed point. Similar conclusions hold for LR correlated disorder in x [21].…”

Section: Pacs Numberssupporting

confidence: 74%

Universal high-temperature regime of pinned elastic objects

2010

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We study the high temperature regime within the glass phase of an elastic object with short ranged disorder. In that regime we argue that the scaling functions of any observable are described by a continuum model with a δ-correlated disorder and that they are universal up to only two parameters that can be explicitly computed. This is shown numerically on the roughness of directed polymer models and by dimensional and functional renormalization group arguments. We discuss experimental consequences such as non-monotonous behaviour with temperature. PACS numbers:Elastic objects pinned by quenched disorder are ubiquitous in nature, e.g. vortex lattices in superconductors [1], magnetic domain walls [2]. They are modeled by elastic manifolds, of internal dimension d, parameterized by a N -component displacement field u(x), submitted to random potentials. These systems have been described using the collective pinning theory [3], in terms of the characteristic Larkin length R c , and more recently using functional renormalization group (FRG) [4,5] in terms of a RG fixed point at zero temperature, with only few universality classes depending on N, d and the nature of elasticity and disorder -short range (SR) or long range (LR). For scales larger than R c these objects exhibit glass phases with statistically self-similar ground states of roughness scaling as u ∼ x ζ and self-similar energy landscape with free energy exponent θ. Whenever θ > 0 the T = 0 fixed point is attractive and thermal fluctuations are irrelevant at low temperature for large systems. In some cases (θ F > 0 see below) the glass phase extends to all temperatures, with, however, a crossover at T = T dep . At high temperature T > T dep , the system unbinds from individual pins but remains collectively pinned, and the Larkin length increases with T [1, 6, 7]. This has interesting consequences, e.g. a reentrant region in the phase diagram of high T c superconductors [9]. It was generally argued that, due to this effect, the roughness amplitude decays with temperature for SR disorder [6,8,10].Besides its interest to experiments, the high temperature regime is also at the center of recent works on the directed polymer (DP) d = 1, a problem in close connection to KPZ growth and Burgers turbulence [11][12][13][14]. In two dimension (N = 1) it is amenable to the Bethe Ansatz method using a continuum model with δ-function correlation in the random potential [15]. Since the collective pinning theory and the FRG show that a finite correlation range in the disorder is an important ingredient to describe pinning, an outstanding question has been the domain of validity of this model. Recently the distribution of the free energy F of polymers of length x was computed within the δ-correlated model [8,13,16,17].At large scale x one recovers the Tracy Widom distribution [19], previously proved to hold [18] for a discrete DP model, but at T = 0. At first sight, it suggests that the δ-function model also captures the universality at low temperature, in agreement with the i...

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“…Since ζ F SR < ζ SR , a finite g guarantees that at high T the system is described by the SR fixed point. Similar conclusions hold for LR correlated disorder in x [21].…”

Section: Pacs Numberssupporting

confidence: 74%

Universal high-temperature regime of pinned elastic objects

2010

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“…It is interesting to note that our estimates coincide, within error bars, with the critical exponents obtained for a stochastic sandpile model in the conserved directed-percolation class [70]. The method applied in the present paper may be used to analyze exponents in different depinning universality classes, such as the long-range elasticity, quenched Kardar-Parisi-Zhang, or correlated disorder classes [71].…”

Section: Discussionmentioning

confidence: 75%

“…In steadystate simulations with dynamically generated disorder, such as the ones in Ref. [36], one should be cautious at long times or large center of mass displacements, because of the critical force extreme statistics, since, in this case, f c can be considered as the maximum among ∼M/L ζ independent typical critical forces [53,54,69]. Therefore, a finite-velocity steady-state might not exist at zero temperature if the critical force statistics tends to Gumbel's type for large M/L ζ for instance, as the interface will eventually be blocked (by virtue of the Middleton theorems [28]) at any finite force.…”

Section: Discussionmentioning

confidence: 99%

Nonsteady relaxation and critical exponents at the depinning transition

2013

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We study the nonsteady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units. We compute the timedependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, nonuniversal microscopic time regime, we find a nontrivial long crossover towards the nonsteady macroscopic critical regime. This "mesoscopic" time regime is robust under changes of the microscopic disorder, including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms, yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L 2 25 ) simulations for the nonsteady dynamics of the continuum displacement quenched Edwards-Wilkinson equation, getting accurate and consistent depinning exponents for this class: β = 0.245 ± 0.006, z = 1.433 ± 0.007, ζ = 1.250 ± 0.005, and ν = 1.333 ± 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent β) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.

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“…This distribution is characterized by its width which decays with the interfacial length and depends only on the strength of the disorder, measured by the prefactor of the disorder two-point correlation function [33].…”

Section: Droplet Spreading and Approach To Pinningmentioning

confidence: 99%

Droplet spreading and pinning on heterogeneous substrates

Alava

Dubé

2012

Phys. Rev. E

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The contact angle of a fluid droplet on an heterogeneous surface is analyzed using the statistical dynamics of the spreading contact line. The statistical properties of the final droplet radius and contact angle are obtained through applications of depinning transitions of contact lines with nonlocal elasticity and features of pinning-depinning dynamics. Such properties not only depend on disorder strength and surface details, but also on the droplet volume and disorder correlation length. Deviations from Wenzel or Cassie-Baxter behavior are particularly apparent in the case of small droplet volumes and small contact angles.

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Universal distribution of threshold forces at the depinning transition

Cited by 34 publications

References 45 publications

Universal high-temperature regime of pinned elastic objects

Universal high-temperature regime of pinned elastic objects

Nonsteady relaxation and critical exponents at the depinning transition

Droplet spreading and pinning on heterogeneous substrates

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